Sheet of wood. one layer of carpet stapled to it at the top, another stapled to the back of the top, then flipped over to the front so it hangs a little bit away, has some movement (which helps absorb any rebounds). This setup has been fine with 12ft/lb rifles.
You could just pin targets to this, but the bullseye will wear through fairly quick (you being an ace shot and everyhting, like me ) so you might like to knock up a pellet catcher from a bit more wood; fill the back of it with plumber's mait which will hold the pellets that hit it (and be very quiet) - just fold it over itself when the pellets start getting dense. Or buy a proper one (usually steel-backed, will make a loud "ting" when you're on-taregt... can annoy the neighbours).